Boys to girls

The ratio of boys to girls at a party is 3:5. If six more boys arrived and four girls left the party, the ratio of boys to girls would be 5:6. How many people were at the party initially?

Correct result:

t =  64

Solution:

$$\begin{gathered} t=a+b \\ a=3\mathrm{/}5\cdot b \\ (a+6)=5\mathrm{/}6\cdot (b-4) \\ a+b-t=0 \\ 5a-3b=0 \\ 6a-5b=-56 \\ a=24 \\ b=40 \\ t=64 \end{gathered}$$

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